Abstract. Let H be a compact subgroup of a locally compact group G, and let be a strongly quasi-invariant Radon measure on the homogeneous space GH. In this article, we show that every element of GH, the char acter space of GH, determines a nonzero multiplicative linear functional on L1(GH ).Using this, we prove that for all GH, the right-amenability of L1(GH ) and the right-amenability of M(GH) are both equivalent to the amenability of G. Also, we show that L1(GH ), as well as M(GH), is right-contractible if and only if G is compact. In particular, when H is the trivial subgroup, we obtain the known results on group algebras and measure algebras.
